Finite Group Databasebeta

← Group #14512512

Character table — Group #14512512

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size13412121212121220326064641201201201201601341212121212122032606464120120120120160
order12521010101010234151544886221021010101010264303044886
χ111111111111111111111111111111111111111
χ211111111111111-1-1-1-1111111111111111-1-1-1-11
χ3111111111-11-111i−ii−i-1111111111-11-111i−ii−i-1
χ4111111111-11-111−ii−ii-1111111111-11-111−ii−ii-1
χ52222222222-12-1-10000-12222222222-12-1-10000-1
χ6222222222-2-1-2-1-100001222222222-2-1-2-1-100001
χ7333-13-1-1-1-130-10011-1-10333-13-1-1-1-130-10011-1-10
χ8333-13-1-1-1-130-100-1-1110333-13-1-1-1-130-100-1-1110
χ9333-13-1-1-1-1-30100i−i−ii0333-13-1-1-1-1-30100i−i−ii0
χ10333-13-1-1-1-1-30100−iii−i0333-13-1-1-1-1-30100−iii−i0
χ1144-14-1-1-1-1-1040-1-10000044-14-1-1-1-1-1040-1-100000
χ1244-14-1-1-1-1-10-201−i1521+i1520000044-14-1-1-1-1-10-201−i1521+i15200000
χ1344-14-1-1-1-1-10-201+i1521−i1520000044-14-1-1-1-1-10-201+i1521−i15200000
χ141212-3-4-3111100000000001212-3-4-311110000000000
χ1512-4120-40000000000000012-4120-400000000000000
χ1612-4-301−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58000000000012-4-301−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ580000000000
χ1712-4-3013ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ58000000000012-4-3013ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ580000000000
χ1812-4-301−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58000000000012-4-301−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ580000000000
χ1912-4-301−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58000000000012-4-301−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ580000000000
χ201111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ22111111111-11-111i−ii−i-1-1-1-1-1-1-1-1-1-11-11-1-1−ii−ii1
χ23111111111-11-111−ii−ii-1-1-1-1-1-1-1-1-1-11-11-1-1i−ii−i1
χ242222222222-12-1-10000-1-2-2-2-2-2-2-2-2-2-21-21100001
χ25222222222-2-1-2-1-100001-2-2-2-2-2-2-2-2-2212110000-1
χ26333-13-1-1-1-130-10011-1-10-3-3-31-31111-30100-1-1110
χ27333-13-1-1-1-130-100-1-1110-3-3-31-31111-3010011-1-10
χ28333-13-1-1-1-1-30100i−i−ii0-3-3-31-3111130-100−iii−i0
χ29333-13-1-1-1-1-30100−iii−i0-3-3-31-3111130-100i−i−ii0
χ3044-14-1-1-1-1-1040-1-100000-4-41-4111110-401100000
χ3144-14-1-1-1-1-10-201−i1521+i15200000-4-41-411111020−1+i152−1−i15200000
χ3244-14-1-1-1-1-10-201+i1521−i15200000-4-41-411111020−1−i152−1+i15200000
χ331212-3-4-311110000000000-12-12343-1-1-1-10000000000
χ3412-4120-400000000000000-124-120400000000000000
χ3512-4-301−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ580000000000-12430-1ζ2+ζ14+ζ22−3ζ26+ζ34+ζ38−3ζ46+ζ58−3ζ2+ζ14−3ζ22+ζ26+ζ34+ζ38+ζ46+ζ58ζ2−3ζ14+ζ22+ζ26−3ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22+ζ26+ζ34−3ζ38+ζ46−3ζ580000000000
χ3612-4-3013ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ580000000000-12430-1−3ζ2+ζ14−3ζ22+ζ26+ζ34+ζ38+ζ46+ζ58ζ2−3ζ14+ζ22+ζ26−3ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22+ζ26+ζ34−3ζ38+ζ46−3ζ58ζ2+ζ14+ζ22−3ζ26+ζ34+ζ38−3ζ46+ζ580000000000
χ3712-4-301−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ580000000000-12430-1ζ2−3ζ14+ζ22+ζ26−3ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22+ζ26+ζ34−3ζ38+ζ46−3ζ58ζ2+ζ14+ζ22−3ζ26+ζ34+ζ38−3ζ46+ζ58−3ζ2+ζ14−3ζ22+ζ26+ζ34+ζ38+ζ46+ζ580000000000
χ3812-4-301−ζ2−ζ14−ζ22−ζ26−ζ34+3ζ38−ζ46+3ζ58−ζ2−ζ14−ζ22+3ζ26−ζ34−ζ38+3ζ46−ζ583ζ2−ζ14+3ζ22−ζ26−ζ34−ζ38−ζ46−ζ58−ζ2+3ζ14−ζ22−ζ26+3ζ34−ζ38−ζ46−ζ580000000000-12430-1ζ2+ζ14+ζ22+ζ26+ζ34−3ζ38+ζ46−3ζ58ζ2+ζ14+ζ22−3ζ26+ζ34+ζ38−3ζ46+ζ58−3ζ2+ζ14−3ζ22+ζ26+ζ34+ζ38+ζ46+ζ58ζ2−3ζ14+ζ22+ζ26−3ζ34+ζ38+ζ46+ζ580000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.